The group is led by Xiaohui Liu, who currently holds the position of Professor in the Physics Department at Beijing Normal University. Previously, Liu was a T.D. Lee Fellow at the Center for High Energy Physics, at Peking University. Our research focuses mainly on particle physics and high-energy nuclear physics, with an emphasis on applying the fundamental principles of Quantum Chromodynamics to predict collider phenomenologies.
here is a List of Liu's Publications and Liu's Google research profile
Quantum Field Theory (Spring, 2019)
The course is designed at the introductory level to the quantum field theory for the graduate students at Beijing Normal University. The lecture notes and homework sets will be posted here.
Lecture notes
- lecture 1 (quantum harmonic oscillator as a 1+0 D field theory: canonical quantization, perturbation theory, asymptotic series, Feynman diagrams)
- lecture 2 (quantum harmonic oscillator as a 1+0 D field theory: Wick Theorem, Feynman rules, Parth integral)
- lecture 3 (quantum harmonic oscillator as a 1+0 D field theory: Parth integral, Instanton, Dilute Instanton Gas)
References: Coleman, The Uses of Instantons; Landau, Lifshitz, QM (2nd edition), chapter 23 problem 4, for solving K (discrete spectrum) and chapter 25 problem 5, for continuous spectrum. Find another reference on this with more details: Shifman, et. al., ABC of Instantons. Also here is a material for highlighting the numerical power and method of Path Integral (imaginary time): Lepage, Lattice QCD for Novices (chapeter 2 + exercise), which I hope you will appreciate.
- lecture 4 (relativisitic quantum mechanics: its difficulties)
- lecture 5 (review of Classic Field theory, Electrodynamics)
- lecture 6 (Gauge Symmetry,Canonical quantization of free E&M field in coulomb gauge)
- lecture 7 (infinities,infinities,infinities! the idea of renormalization from an effective theory point of view, Casimir effects)
References:a measurement of the Casimir forcer and different voices. A note on the Euler-Maclaurin formula taken from Guth’s QFT note, for understanding the regulator independnece. A very nice TASI lecture note on effective theory by Polchinski, which may be too much for beginners though.
- lecture 8 (let’s turn on interactions, QFT+QM, lamb shift, mass renormalization)
References: We follow Bethe’s original paper but we add more comments on the validity of the integration bound choice. A more rigorours QFT derivation of the Lamb Shift can be found in Weinberg’s QFT book, Ch 14, but it is too advanced for this course.
Homework
References
There are plenty open resources on QFT online, including the famous lectures by Sydney Coleman hosted by Harvard. Some of the topics in this course can be found in
- M. Srednicki, Quantum Field Theory.
- Matt. Schwartz, Quantum Field Theory and Standard Model.
- S. Weinberg, The Quantum Theory of Fields.
- Peskin & Dan Schroeder, An Introduction To Quantum Field Theory.